ASTRONOMY AND METEOROLOGY. 407 



overbalance the diminished amount at another part, and the less is the total 

 amount of the sun's disturbing force. And as the sun's disturbing force 

 diminishes the moon's attraction to the earth, that attraction is less and less 

 impaired every century, or becomes practically stronger; every century the 

 moon is pulled into a rather smaller orbit, and revolves in a rather shorter 

 period. On computing the effect from this cause, it was found to airree well 

 with the effect which Halley and Dunthorne had discovered in observations. 

 The lunar tables thus amended, and with other but minor improvements, 

 were applied to the computation of other ancient eclipses, which require far 

 greater nicety than Ptolemy's lunar eclipses, namely, total eclipses of the sun. 

 The most remarkable of these were the eclipse of Thales (which occurred at 

 a battle), that at Larissa, or Nimrud (which led to the capture of that city by 

 the Persians from the Medes), and that of Agathocles (upon a fleet at sea). 

 They are all of great importance in settling the chronology. Dates were 

 thus found for these several eclipses, which are most satisfactory. About 

 this time Mr. Adams announced his discovery, that a part of the sun's dis- 

 turbing force had been omitted by Laplace. The sun pulls the moon in the 

 direction in which she is going (so as to accelerate her) in some parts of her 

 orbit, and in the opposite direction (so as to retard her) in other parts. La- 

 place and others supposed that those accelerations and retardations exactly 

 balance. Mr. Adams gave reason for supposing that they do not balance. 

 In this he was subsequently supported by M. Delaunay, a very eminent 

 French mathematician, who, making his calculations in a different way, 

 arrived at the very same figures. But he is opposed by Baron Plana, by the 

 Count de Pontecoulant, and by Professor Hansen, who all maintain that 

 Laplace's investigations are sensibly correct. And in this state the contro- 

 versy stands at present. It is to be remarked, that observations can here 

 give no assistance. The question is purely whether certain algebraical 

 investigations are right or wrong. And it shows that what is commonly 

 called " mathematical evidence" is not so certain as many persons imagine, 

 and that it ultimately depends on moral evidence. The effect of Mr. Adams's 

 alteration is to diminish Laplace's change of the periodic time by more than 

 one-third part. The computations of the ancient eclipses are very sensibly 

 affected by this. At present we can hardly say how much they are affected; 

 possibly those of Larissa and Agathocles would not be very much disturbed ; 

 but it seems possible that the computed eclipse of Thales might be thrown 

 so near to sunset as to be inapplicable to elucidation of the historic account. 

 This is the most perplexing eclipse, because it does not appear that any other 

 eclipse can possibly apply to the same history. The interest of this subject, 

 it thus appears, is not confined to technical astronomy, but extends to other 

 matters of very wide range. And the general question of the theory of the 

 moon's acceleration may properly be indicated as the most important of the 

 subjects of scientific controversy at the present time. 



ON THE SECULAR PERTURBATIONS OF FOUR OF THE ASTEROIDS. 



The following is a reported abstract of a paper on the above subject pre- 

 sented to the American Association for the Promotion of Science by Mr. S. 

 Newcomb, of Cambridge : 



Dr. Olbers supposed that the numerous small planets circulating between 

 Mars and Jupiter were the fragments of a large one which had been shat- 

 tered through the agency of some unknown cause. If this hypothesis were 



